The present invention relates to beam propagation method and, more particularly, to a method and apparatus for designing planar lightwave circuits using beam propagation methods.
Planar lightwave circuits are well-suited for mass production of optical filters and switches. Planar lightwave circuits, such as step-index waveguides, typically consist of a substrate, a uniform lower cladding, a core that varies discretely in two dimensions, and a uniform upper cladding. Beam propagation methods (BPM) are utilized to investigate lightwave propagation through simulated planar lightwave circuits. For a review of general beam propagation methods, see, for example, K. Okamoto, Fundamentals of Optical Waveguides, Chapter 7, Academic Press (2000), incorporated by reference herein. The two most popular beam propagation methods used in the design of planar lightwave circuits are the split-step Fourier Transform beam propagation method, often referred to as the Fast Fourier Transform (FFT)-BPM, and the finite-difference beam propagation method (FD-BPM).
Generally, the FFT-BPM and FD-BPM both approximate a planar waveguide structure by plotting the index of refraction as a function of the spatial coordinates using a spatial grid. Thus, spatial quantization errors are introduced along the waveguide boundaries between the core and the cladding. In addition, the FFT-BPM and FD-BPM both permit simulation of planar lightwave circuits having an arbitrary index distribution, i.e., an arbitrary core cross section. In addition, the FFT-BPM continuously translates between the spatial domain and angular spectrum domain using Fourier transform techniques. Thus, these beam propagation methods have significant processing speed and memory capacity requirements. A need therefore exists for beam propagation methods with reduced computational complexity and spatial quantization errors.
Generally, a novel beam propagation method and design tool are disclosed that are based on the FFT-BPM. The present invention provides a beam propagation method that is constrained to planar waveguides having a rectangular cross-section, resulting in significantly reduced computational complexity and better accuracy. Among other benefits, the beam propagation method can be performed entirely in the angular spectrum domain, without translating back and forth to the spatial domain. In addition, the constrained shape of the waveguide allows the structure to be accurately specified by its width and center-to-center arm spacing, thereby avoiding transverse spatial quantization.
A more complete understanding of the present invention, as well as further features and advantages of the present invention, will be obtained by reference to the following detailed description and drawings.